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Routing overlay offers an ideal methodology to improve the end-to-end communicating performance by providing a backup path for any pair of nodes. The current solutions, however, suffer from the simultaneous failures between the default and the selected backup paths. This paper focuses on a crucial issue of selecting a proper backup path to detour around the failures on the default path with high probability. Experiments were conducted to clarify the influence of overlaps between the default and backup paths, which indicated that the overlaps were the root cause of such simultaneous failures. Therefore, we propose ABPS to select a one-hop backup path with both lower communicating delay and less overlaps with the default path. It employs the traceroute probing to enable each node to acquire IP-level path information of the default paths to the other nodes in a full-mesh overlay network. Meanwhile, with the help of Grid Quorum System, when each node distributes its probing results, there is at least one rendezvous node receives enough information for further discovering a backup path for arbitrary pair of nodes. The evaluation results show that ABPS succeeds in improving the availability of the selected backup paths. And the simultaneous failure probability is reduced by about 50 percent, while the fraction of overlapping between the backup path and the default one is dramatically reduced.